
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
The diagram shows a karting track layout. The start and finish are at point \(A\), and the kart driver can enter and leave point \(A\) as many times as desired during the drive.

The route from \(A\) to \(B\) or back takes the young racer Yura one minute. The circular path also takes Yura one minute. On the circular path, driving is allowed only in a counterclockwise direction (the arrows indicate the possible directions of movement). Yura does not turn back halfway and does not stop. The duration of the race is 10 minutes. Find the number of possible different routes (sequences of segments traversed).

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