
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 the sequence \(\{a_{n}\}\) such that \(a_{1}=3\) and for any positive integers \(m, n\), it satisfies \(a_{m+n}=a_{m}+a_{n}+2 mn\).
1. Find the general term formula for the sequence \(\{a_{n}\}\).
2. If the real number \(c\) makes \(\sum_{i=1}^{k} \frac{1}{a_{i}}<c\) valid for all positive integers \(k\), find the range of values for \(c\).

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