
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 $a$, $b$, $c$ satisfy $\sqrt{8-a}+\sqrt{a-8}=|c-17|+b^{2}-30b+225$,
(1) Find the values of $a$, $b$, $c$;
(2) Can a triangle be formed with sides $a$, $b$, $c$? If a triangle can be formed, find the perimeter and area of the triangle; if a triangle cannot be formed, please explain the reason.

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