
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-2| - |x+a|, where a > 0.
1. Find the range of the function f(x).
2. For any real numbers b and c that satisfy b² + c² + bc = 1, the inequality f(x) ≥ 3(b+c) always has a solution. Find the range of a.

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