
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 functions $f(x)=|x^{2}-a|$ and $g(x)=x^{2}-ax$, where $a\in\mathbb{R}$.
1. When $a=1$, find the maximum value of $f(x)$ on the interval $[-1,1]$.
2. Find the minimum value of the maximum value of $f(x)$ on the interval $[-1,1]$, denoted as $M(a)$.
3. If the equation $f(x)+g(x)=0$ has two solutions in the open interval $(0,2)$, find the range of possible values for $a$.

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