
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 $f(x)= \begin{cases}x-1,0 < x\leqslant 2 \\ -1,-2\leqslant x\leqslant 0 \end{cases}$, and $g(x)=f(x)+ax$, where $x\in[-2,2]$, if $g(x)$ is an even function, find the value of the real number $a$.

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