
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| - |x + 1|.
(1) When a = 3, find the solution set of the inequality f(x) ≥ 2x + 3.
(2) If there exists an x in the interval [1, 2] such that f(x) ≤ |x - 5| holds true, find the range of possible values for a.

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