
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
Laura is putting together the following list:  $a_0, a_1, a_2, a_3, a_4, ..., a_n$ , where  $a_0 = 3$  and  $a_1 = 4$ .
She knows that the following equality holds for any value of  $n$  integer greater than or equal to  $1$ :  $$ a_n^2-2a_{n-1}a_{n+1} =(-2)^n. $$  Laura calculates the value of  $a_4$ . What value does it get?

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