
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 \( x \) and \( y \) be positive integers such that \( 5x^7 = 13y^{17} \). The minimum possible value of \( x \) has a prime factorization \( a^c b^d \). What is \( a + b + c + d \)?
A) 30
B) 31
C) 32
D) 33
E) 34

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