
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
Andrey and Boris are playing the following game. Initially, a robot is located at point \( p \) on a number line. First, Andrey states the distance by which the robot should move. Then, Boris chooses the direction in which the robot moves by that distance, and so on. For which values of \( p \) can Andrey ensure that the robot will reach either point 0 or point 1 in a finite number of moves regardless of Boris's actions?

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