
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 inequality $\frac{4}{x} + \frac{9}{5-x} \geqslant m$ which holds true for $x \in (0, 5)$.

(1) Find the maximum value of $m$.
(2) When $m$ takes its maximum value, find the solution set of the inequality $|x - m| + |x + 2| \leqslant 9$.

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