
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 points $A(1,m)$ and $B(1,2\sqrt{5}-m)$, if there exists only one point $P$ on the circle $C:x^{2}+y^{2}+2x=0$ such that $PA\perp PB$, then one possible value of the real number $m$ is _____. (Provide one value that satisfies the condition)

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