
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
Andrei and Boris are playing the following game. Initially, a robot is located at point \( p \) on the number line. First, Andrei states a distance by which the robot should move. Then, Boris chooses the direction in which the robot will move that distance, and so on. For which values of \( p \) can Andrei 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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