
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 that $f(x)$ is an odd function defined on $x\in [-1,1]$, and when $x\in (0,1]$, $f(x)=x^{2}+2x+3$.  
$(1)$ Find the analytical expression of $f(x)$.  
$(2)$ Find the range of $f(x)$.

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