
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 new sequence of integers where $a_i = 2i$ for $1 \le i \le 3$, and for $i > 3$ the sequence is defined as:
\[ a_i = 2 \cdot a_1 a_2 \dotsm a_{i-1} - 2 \]
Evaluate the expression $a_1 a_2 \dotsm a_7 - \sum_{i=1}^7 a_i^2$.

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