
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 + a| + |2x - 3| (a > 0).
(1) Solve the inequality f(x) ≥ 4 when a = 1.
(2) Find the range of real number a such that the inequality f(x) ≤ |x + 3| always holds when x ∈ [a, 2a - 1].

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