
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
Alexey invented the following game. First, he chooses a number \( x \) such that \( 2017 \leqslant x \leqslant 2117 \). Then he checks if \( x \) is divisible by 3, 5, 7, 9, and 11 without a remainder. If \( x \) is divisible by 3, he awards the number 3 points; if by 5, 5 points; ..., if by 11, 11 points. The points earned for the number are summed. Which number should be chosen in this game to earn the maximum number of points?

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