
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 functions: $f(x) = 3x^2 - 2mx - 1$, $g(x) = |x| - \frac{7}{4}$.  
(1) Solve the inequality $f(x) \geq -2$;  
(2) If for any $x \in [0, 2]$, $f(x) \geq g(x)$, find the range of values for $m$.

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