
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
Given $4x^7 = 13y^{17}$ where $x$ and $y$ are positive integers, find the value of $a + b + c + d$ for the prime factorization $a^cb^d$ of the minimum possible value of $x$.

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