
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
Suppose the function $f(x) = |x - 3| - |x - a|$.

(1) Solve the inequality $f(x) \leq -\frac{1}{2}$ when $a = 2$.

(2) If there exists a real number $a$ such that the inequality $f(x) \geq a$ holds, find the range of values for $a$.

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