
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 a function \\(f(x)\\) defined on \\(\mathbf{R}\\) that satisfies: for any real numbers \\(x\\) and \\(y\\), it always holds that \\(f(x)f(y) = f(x+y)\\), and \\(f(1) = 2\\), find \\(f(10)\\).

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