
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 - 1|.
(1) Solve the inequality f(x) ≤ x + 2;
(2) If g(x) = |3x - 2m| + |3x - 1|, for any x₁ ∈ R, there exists x₂ ∈ R such that f(x₁) = g(x₂) holds true, find the range of values for the real number m.

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