
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
The Sequence  $\{a_{n}\}_{n \geqslant 0}$   is defined by  $a_{0}=1, a_{1}=-4$  and  $a_{n+2}=-4a_{n+1}-7a_{n}$  , for  $n \geqslant 0$ . Find the number of positive integer divisors of  $a^2_{50}-a_{49}a_{51}$ .

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