
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 an arithmetic sequence $a_n$ with a common difference $d < 0$, if $a_3a_7 = 9$ and $a_1 + a_9 = 10$, then the maximum value of the sum of the first $n$ terms of this sequence, $S_n$, is.

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