
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
A scientist has invented a time machine that resembles a circular subway track. The present (2010) is the first station. The stations from 2, 3, up to 2009 correspond to the years 2011, 2012, up to 4018, and the 2010th station brings you back to the present (the starting station). However, due to a program error, the operation of the machine has changed as follows: the passenger specifies a time (station number), the machine first reaches that specified station, and then stops at every 5th station. If the station number where it stops is a power of 2, it moves back 2 stations and stops. If it stops at the first station, it stops functioning.

Questions:
(1) Can this machine get lost in the time track and never return to the present (i.e., never stop at the first station)?
(2) If it can eventually return to the present, what is the maximum number of stations it can stop at?

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