
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
A sequence of integers \(\left\{a_{i}\right\}\) is defined as follows: \(a_{i}=i\) for all \(1 \leq i \leq 5\), and \(a_{i}=a_{1} a_{2} \cdots a_{i-1}-1\) for all \(i>5\). Evaluate \(a_{1} a_{2} \cdots a_{2011}-\sum_{i=1}^{2011} a_{i}^{2}\).

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