
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 - 3| - t, where t ∈ R.
1. Solve the inequality |f(x)| ≥ 3 when t = 3.
2. If the solution set of the inequality f(x + 2) ≤ 0 is [-1, 3], and the positive numbers a and b satisfy the equation ab - 2a - 8b = 2t - 2, find the minimum value of a + 2b.

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