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The union representing the train drivers involved in a pay dispute with ScotRail says it is hopeful that a resolution is possible this week.
Aslef and ScotRail's latest talks were adjourned after a 90-minute meeting.
The drivers' union Aslef rejected the train operator's latest 4.2% pay offer last week, but is expected to return to discussions later in the week.
The dispute has had a major impact on services, after drivers refused to work on their rest days.
It led to ScotRail introducing a temporary, greatly-reduced timetable to provide "greater certainty".
The rail operator was nationalised by the Scottish government in April.
Kevin Lindsay, Aslef's Scotland organiser, told BBC Scotland both sides had a "bit of work to do".
"Both sides have explored what was on the table previously - how we can re-jig it to see if we can make an improved offer," he said.
"Both sides have tabled ideas and both sides are now away to look at them and will resume talks later in the week."
He added: "If ScotRail continue to talk in the manner they are talking I can see us reaching somewhere, but if they don't I can see us reaching industrial action."
Aslef members had met in Perth on Sunday ahead of negotiations with ScotRail resuming this week.
A temporary, scaled-back Sunday timetable was introduced at the weekend, following several weeks of severe disruption.
Despite that, dozens of services were cancelled and others were terminated part way through their route.
Passengers attending events at Glasgow's SEC and Hydro were asked to check their travel plans in advance.
The last train to the city centre was due to leave the Exhibition Centre train station at 21:03 - half an hour before the end of Michael Flatley's Lord of the Dance at the SEC Armadillo.
Reduced Monday-Saturday ScotRail timetables have been in place since last month.
They have almost 700 fewer services a day, with the last train on many routes leaving up to four hours earlier than before.
Exactly what Aslef is looking for is something of a mystery. The union says it doesn't want to negotiate via the media, so it is not letting on publicly.
Last week, ScotRail's offer included a promise of no compulsive redundancies for three years, while another part of it was enhanced maternity and adoption leave.
Would it need to be an improvement on that 4.2% pay offer or might other improvements to conditions of service prove satisfactory?
The problem of offering a bigger pay rise - apart from questions of affordability with ScotRail back in public ownership - is it's hard to offer more to ScotRail staff while public sector workers such as teachers and council workers are only being offered a 2% rise.
Council unions already said last week they would be balloting for a strike.
If the talks conclude without an agreement a ballot on strike action seems inevitable.
The timescale to allow for running that ballot - and provide notice of any action - would mean it would probably be August before there could be a strike.
There would still be plenty of be time to avoid it, but whether a resolution can be found is another matter entirely.
Aslef has previously rejected a 2.2% pay offer, before later being offered 4.2% and improved conditions - which Transport Minister Jenny Gilruth said she was "hopeful" would be accepted.
But the union announced on Wednesday that its national executive had rejected the offer and would ballot for industrial action unless further talks were held.
ScotRail said it was frustrated by the decision, and "astonished" that the union had decided not to put the improved pay offer to its members.
It said the "substantially improved" offer reflected the cost-of-living challenges faced by families across the country, while balancing it against the need to provide value for the taxpayer.
Transport Scotland - the government's transport agency - described the latest offer as being "both fair and affordable".
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