
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 proposition $p$: $(x+1)(x-5) \leqslant 0$, and proposition $q$: $1-m \leqslant x+1 < 1+m$ where $m > 0$.  
(1) If $\neg p$ is a sufficient condition for $\neg q$, determine the range of the real number $m$.  
(2) If $m=5$, and the proposition "$p \vee q$" is true while "$p \land q$" is false, determine the range of the real number $x$.

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