
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
Consider an arithmetic sequence $\{{a_n}\}$ that satisfies ${a_2}=9$, and ${a_1}, {a_5}$ are the two roots of the equation ${x^2}-16x+60=0$.
(1) Find the general term formula for $\{{a_n}\}$;
(2) Find the maximum sum of the first $n$ terms and the number of terms in this sum.

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