
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
Let \(x = \sqrt{\frac{\sqrt{37}}{2} + \frac{3}{2}}.\) There exist unique positive integers \(a, b, c\) such that
\[x^{80} = 2x^{78} + 8x^{76} + 9x^{74} - x^{40} + ax^{36} + bx^{34} + cx^{30}.\] Find \(a + b + c.\)

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