
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
Suppose \( f(x) \) is defined for \( x > 0 \), with \( f(2) = 1 \) and \( f(xy) = f(x) + f(y) \). Additionally, \( f(x) > f(y) \) if and only if \( x > y > 0 \). Find:
1. The values of \( f(1) \) and \( f(4) \).
2. The range of \( x \) for which \( f(x) + f(x-3) \leq 2 \).

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