
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 $\left|x-2\right| < a\left(a\in\mathbb{N}^*\right)$, 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 $f\left(x\right)=\left|x+a\right|+\left|x-2\right|$.

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