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

1. Solve the inequality f(x) ≤ 5.
2. If there exists x₀ ∈ [1, +∞) such that $f(x₀) + m ≤ x₀ + \frac{3}{x₀}$ 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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