
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 a sequence ${a_n}$ with its sum of the first $n$ terms denoted as $S_n$, if $a_n + a_{n+2} = 2a_{n+1}$ and $a_1 = 13$, $a_2 = 11$, find the value of $n$ when $S_n$ reaches its maximum.

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