
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 $f(x)=|ax+1|$ where $a\in R$, the solution set of the inequality $f(x)\leqslant 3$ is $\\{x|-2\\leqslant x\\leqslant 1\\}$.

(I) Find the value of $a$;

(II) If the function $g(x)=f(x)-|x+1|$, find the minimum value of $g(x)$.

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