
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
\( f \) is a function that maps positive integers to positive integers, \( f(1)=5 \). It satisfies the equation \( f(m+n)=f(m)+f(n)+5mn-1 \) for all \( m, n \in \mathbb{N}_{+} \). Find \( f(n) \).

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