
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 $y=2x^{2}-\left(m+2\right)x+m$ (where $m$ is a constant), when $-2\leqslant x\leqslant 2$, the minimum value of $y$ is denoted as $a$. The value of $a$ changes with the value of $m$. Find the value of $m$ when $a$ reaches its maximum.

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