
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) = |x - 1| - |2x + 3|.

1. Solve the inequality f(x) ≥ x + 1.
2. Let the maximum value of function f(x) be m. If $\frac{1}{a^2} + \frac{4}{b^2} + \frac{9}{c^2} = 2m - 4$, find the maximum value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$.

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