
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
$$
f(x)=\left(a+\frac{1}{a}\right) \ln x+\frac{1}{x}-x .
$$
(1) Let \( a > 1 \). Discuss the monotonicity of \( f(x) \) on the interval \( (0,1) \);
(2) Let \( a > 0 \). Find the extremum of \( f(x) \).

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