
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 the sum of the first \( n \) terms as \( S_n \), if \( a_1 > 0 \) and \( a_1 + 9a_6 = 0 \), then when \( S_n \) takes its maximum value, \( n \) is ( ).

A． 11 B． 10 C． 6 D． 5

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