
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 $f(x) = |x-5| - |x-2|$.
(1) If there exists $x \in \mathbb{R}$ such that $f(x) \leq m$ holds, find the range of $m$;
(2) Find the solution set of the inequality $x^2 - 8x + 15 + f(x) \leq 0$.

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