
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
How many sequences of integers \(\left(a_{1}, \ldots, a_{7}\right)\) are there for which \(-1 \leq a_{i} \leq 1\) for every \(i\), and
$$
a_{1} a_{2} + a_{2} a_{3} + a_{3} a_{4} + a_{4} a_{5} + a_{5} a_{6} + a_{6} a_{7} = 4 ?
$$

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