
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
(The full score of this question is 12 points)

Given $P=\{x|x^2-8x-20\leq0\}$, $S=\{x|1-m\leq x\leq 1+m\}$

(1) Does there exist a real number $m$ such that $x\in P$ is a necessary and sufficient condition for $x\in S$? If it exists, find the range of $m$.

(2) Does there exist a real number $m$ such that $x\in P$ is a necessary condition for $x\in S$? If it exists, find the range of $m$.

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