
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+m|, where m is a real number:
1. Solve the inequality f(x) ≤ 3 when m = 2.
2. Find the range of real number m values such that the inequality f(x) ≤ |2x - 3| has a solution in the interval x ∈ [0, 1].

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