
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 is defined as follows: $a_i = i$ for $1 \le i \le 2,$ and
\[a_i = a_1 a_2 \dotsm a_{i - 1} - 1\]for $i > 2.$  Evaluate $a_1 a_2 \dotsm a_{100} - \sum_{i = 1}^{100} a_i^2.$

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