
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 that f(x) = |x|,

1. Solve the inequality f(2x - 3) ≤ 5;
2. If x² + 2x + f(x - 2) + f(x + 3) ≥ a + 1 is always true for x ∈ [-1, 3], find the range of values for the real number a.

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