
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
Given two points $A$ and $B$ on the number line corresponding to numbers $-1$ and $3$, respectively, and point $P$ as a moving point on the number line with a corresponding number $x$; $O$ is the origin.<br/>① If the distance from point $P$ to points $A$ and $B$ are equal, find the number corresponding to point $P$;<br/>② Does there exist a point $P$ on the number line such that the sum of the distances from point $P$ to points $A$ and $B$ is $5$? If so, find the value of $x$;<br/>③ When point $P$ moves to the left from point $O$ at a speed of $1$ unit length per minute, point $A$ moves to the left at a speed of $5$ units per minute, and point $B$ moves to the left at a speed of $20$ units per minute, at what minute(s) will the distance from point $P$ to points $A$ and $B$ be equal? (Write down the result directly)

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