
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 the function $f\left(x\right)$ is an even function defined on $\left[-5,5\right]$, and when $0\leqslant x\leqslant 5$, $f\left(x\right)=x^{2}-4x$.  
$(1)$ Find the value of $f\left(-3\right)$ and the analytical expression of $f\left(x\right)$;  
$(2)$ Find the range of $f\left(x\right)$ on $\left[-5,5\right]$.

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