
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 $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$, given that $a_1=2$, and for any $p$, $q \in \mathbb{N}^*$, it holds that $a_{p+q}=a_p+a_q$. Then, the minimum value of $f(n)=\frac{S_n+60}{n+1}$ $(n \in \mathbb{N}^*)$ is ______.

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