
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: $a_i = i^2$ for $1 \le i \le 4,$ and
\[a_i = a_1 a_2 \dotsm a_{i - 1} - i\]for $i > 4.$  Evaluate $a_1 a_2 \dotsm a_{100} - \sum_{i = 1}^{100} a_i^2.$

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