
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 $f(x)=2a^{2}\ln x-x^{2}$ (where $a > 0$).
(1) Find the equation of the tangent line to the curve $y=f(x)$ at $x=1$ when $a=1$.
(2) Discuss the number of zeros of the function $f(x)$ in the interval $(1,e^{2})$ ($e$ is the base of the natural logarithm).

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