
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 $a < 0$ is a real number, the function $f(x)=a \sqrt{1-{x}^{2}}+ \sqrt{1+x}+ \sqrt{1-x}$.
(1) Let $t= \sqrt{1+x}+ \sqrt{1-x}$, determine the range of $t$;
(2) Express $f(x)$ as a function of $t$, denoted as $h(t)$;
(3) If the maximum value of function $f(x)$ is $g(a)$, determine $g(a)$.

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