
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) = |mx + 1| + |2x - 3|.
(1) When m = 2, find the range of x values for which f(x) = 4.
(2) If $f(1) \leq \frac{2a^2 + 8}{a}$ holds true for any positive real number a, find the range of real number m values.

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