
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 that $a > 0$, $b > 0$, and $a + b = 1$.

(1) If $ab \leq m$ always holds true, find the range of values for the real number $m$.

(2) If the inequality $\frac{4}{a} + \frac{1}{b} \geq |2x - 1| - |x + 2|$ always holds true, find the range of values for $x$.

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