
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: $b_i = i^2$ for $1 \le i \le 3,$ and
\[b_i = b_1 b_2 \dotsm b_{i - 1} + 1\]for $i > 3.$  Evaluate $b_1 b_2 \dotsm b_6 - \sum_{i = 1}^{6} b_i^2.$

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