
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 \( f \) is a function that satisfies \( f(2) = 20 \) and \( f(2n) + n f(2) = f(2n+2) \) for all positive integers \( n \). What is the value of \( f(10) \)?

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