
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 robot is placed on a point $P$ on a number line, excluding the points $0$ and $1$. The robot can only move left or right along the number line. Two players, A and B, play the following game: Player A specifies a distance, and Player B specifies a direction. The robot then moves in the specified direction by the specified distance. Player A's goal is to move the robot to point $0$ or $1$, while Player B's goal is to prevent Player A from achieving this. When does Player A have a winning strategy given the position $P$ of the robot?

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