
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
If \(a\), \(b\), \(c\), \(d\), \(e\), and \(f\) are integers for which \[1728x^3+64 = (ax^2 + bx + c)(dx^2 + ex + f)\] for all \(x\), then what is \(a^2+b^2+c^2+d^2+e^2+f^2\)?

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