
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
Elective 4-5: Selected Topics on Inequalities:  
(1) Given $f(x) = |x-a|$, if the solution set of the inequality $f(x) \leq 2$ is $\{x|-1 \leq x \leq 3\}$, find the value of $a$;  
(2) If $\log_{2}(|x-a|+|x-3|) \geq 2$ always holds, find the range of the real number $a$.

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