
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
Let \\(f(x)\\) be a monotonically increasing function defined on \\((0,+\infty)\\) that satisfies \\(f(xy)=f(x)+f(y)\\) and \\(f(3)=1\\). Find:  
\\((1)\\) \\(f(1)\\);  
\\((2)\\) If \\(f(x)+f(x-8) \leqslant 2\\), find the range of \\(x\\).

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