
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
Given an integer sequence \(\{a_i\}\) defined as follows:
\[ a_i = \begin{cases} 
i, & \text{if } 1 \leq i \leq 5; \\
a_1 a_2 \cdots a_{i-1} - 1, & \text{if } i > 5.
\end{cases} \]

Find the value of \(\sum_{i=1}^{2019} a_i^2 - a_1 a_2 \cdots a_{2019}\).

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