
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
Among the first hundred elements of the arithmetic progression \(3, 7, 11, \ldots\), find those that are also elements of the arithmetic progression \(2, 9, 16, \ldots\). Provide the sum of the found numbers in your answer.

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