
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
It is known that the function $f(x) = |2x+1| + |3x-2|$, and the solution set of the inequality $f(x) \leq 5$ is $\left\{x \middle| -\frac{4a}{5} \leq x \leq \frac{3b}{5}\right\}$, where $a, b \in \mathbb{R}$.
(1) Find the values of $a$ and $b$;
(2) For any real number $x$, the inequality $|x-a| + |x+b| \geq m^2 - 3m + 5$ holds. Find the maximum value of the real number $m$.

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