
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 - 2|, where a is a real constant.

1. If the minimum value of function f(x) is 3, find the value of a.
2. If the inequality f(x) ≤ |x - 4| always holds when x ∈ [1, 2], find the range of a.

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