
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)=\begin{cases}\begin{matrix}1+ \frac{1}{x}(x > 1) \\\\ x^{2}+1(-1\leqslant x\leqslant 1)\\\end{matrix} \\\\ 2x+3(x < -1)\\\end{cases} $.

(1) Find the value of $f\{f[f(-2)]\}$;
(2) If $f(a)= \frac{3}{2} $, find the value of $a$.

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