
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 $f(x)=x^{2}-2ax+2$, where $x\in\[-5,5\]$,
(1) Find the range of real number $a$ such that $y=f(x)$ is a monotonically decreasing function in its domain;
(2) Denote the minimum value of the function $y=f(x$ as $g(a)$, find the analytical expression of $g(a)$.

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