
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Trains circulate in the same direction around a circular track at equal intervals, with stations $A$, $B$, and $C$ located at the vertices of an equilateral triangle (labeled in the direction of travel). Ira boards at station $A$ while Alex boards at station $B$ at the closest train. It is known that if they board at the moment when the train driven by Roma is passing through the forest, Ira will board earlier than Alex; otherwise, Alex will board earlier than Ira or at the same time. What fraction of the track goes through the forest?

Present the answer in LaTex format: \boxed{Your answer}
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