
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 propositions p: $x^2-4x-5\leq0$, and q: $x^2-2x+1-m^2\leq0$ ($m>0$).  
(1) If p is a sufficient condition for q, find the range of real numbers m.  
(2) If $m=5$, and $p\lor q$ is true while $p\land q$ is false, find the range of real numbers x.

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