
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
The expression \( 125x^8 - 2401y^8 \) can be factored as \( (Ax + By)(Cx^4 + Dxy + Ey^4)(Fx + Gy)(Hx^4 + Jxy + Ky^4) \). If \( A \), \( B \), \( C \), \( D \), \( E \), \( F \), \( G \), \( H \), \( J \), and \( K \) are all integers, find their sum.

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