
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 $f(x)=\ln x+ax (a\in R)$.
(1) When $a=- \frac{1}{3}$, find the extreme values of the function $f(x)$ in the interval $[e,e^{2}]$;
(2) When $a=1$, the function $g(x)=f(x)- \frac{2}{t}x^{2}$ has only one zero point. Find the value of the positive number $t$.

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