
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
Brian starts at the point  $\left(1,0\right)$  in the plane. Every second, he performs one of two moves: he can move from  $\left(a,b\right)$  to  $\left(a-b,a+b\right)$  or from  $\left(a,b\right)$  to  $\left(2a-b,a+2b\right)$ . How many different paths can he take to end up at  $\left(28,-96\right)$ ? 

*2018 CCA Math Bonanza Individual Round #14*

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