
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 $f(x) = x^2 - (a + \frac{1}{a})x + 1$,  
(1) If $a > 0$, solve the inequality $f(x) \leq 0$ with respect to $x$;  
(2) If for any $x \in (1, 3)$, the inequality $f(x) + \frac{1}{a}x > -3$ always holds, find the range of values for $a$.

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