
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 even function, and when $x\geqslant 0$, $f\left(x\right)=\begin{cases}x\left(3-x\right),&0\leqslant x\leqslant 3 \\\left(x-3\right)\left(a-x\right),&x > 3\end{cases}$.

1. Find the analytical expression of $f(x)$ when $x < 0$.
2. If the maximum value of the function $f(x)$ in the interval $[-5,5]$ is $g(a)$, find the expression of $g(a)$.

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