
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
Define a sequence of integers where $a_i = 3i$ for $1 \le i \le 10$, and for $i > 10$:
\[a_i = 2a_1 a_2 \dotsm a_{i - 1} - i\]
Evaluate $a_1 a_2 \dotsm a_{2011} - \sum_{i = 1}^{2011} a_i^2$.

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