
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 that $m > 0$, let $p$: $x^{2}-2x-8 \leq 0$, and $q$: $2-m \leq x \leq 2+m$.

(1) If $p$ is a sufficient but not necessary condition for $q$, find the range of real number $m$.

(2) If $m=5$, and the proposition "$p \vee q$" is true while the proposition "$p \wedge q$" is false, find the range of the real number $x$.

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