
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
A function  $f(x)$  satisfies  $f(x)=f\left(\frac{c}{x}\right)$   for some real number  $c(>1)$  and all positive number  $x$ . 

If  $\int_1^{\sqrt{c}} \frac{f(x)}{x} dx=3$ , evaluate  $\int_1^c \frac{f(x)}{x} dx$ 

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