
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) = |2x + 1| + |x - 1|.

1. Solve the inequality f(x) > 2.
2. Let g(x) = f(x) + f(-x). If the inequality |k - 1| < g(x) always holds for any x ∈ R, find the range of the real number k.

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