
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 \(y = \sqrt{\frac{\sqrt{37}}{2} + \frac{5}{2}}.\) There exist unique positive integers \(d\), \(e\), and \(f\) such that
\[y^{50} = 2y^{48} + 6y^{46} + 5y^{44} - y^{25} + dy^{21} + ey^{19} + fy^{15}.\]
Find \(d + e + f.\)

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