
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 - 1|.
(1) Find the solution set for the inequality f(x) ≤ 7.
(3) If the minimum value of the function g(x) = x^2 - 2x + |a^2 - 3| is not less than the minimum value of f(x), find the range of values for a.

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