
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 inequality $|\_x - 2| < \_a \quad (a \in \mathbb{N}^*)$, let the solution set be $A$, and $\frac{3}{2} \in A$, $\frac{1}{2} \notin A$.

(1) Find the value of $a$.

(2) Find the minimum value of the function $f(x) = |\_x + a| + |\_x - 2|$.

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