
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 the function $f(x) = |x-m|-1$.
(1) If the solution set of the inequality $f(x) \leq 2$ is $\{x|-1 \leq x \leq 5\}$, find the value of the real number $m$;
(2) Under the condition of (1), if $f(x) + f(x+5) \geq t-2$ holds true for all real numbers $x$, find the range of the real number $t$.

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