
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
\( f(x) \) is an increasing function defined on \( (0, +\infty) \), and it satisfies \( f\left(\frac{x}{y}\right) = f(x) - f(y) \).

(1) Find the value of \( f(1) \).

(2) Given that \( f(6) = 1 \), solve the inequality \( f(x+3) - f\left(\frac{1}{x}\right) < 2 \).

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