
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 the function $f(x) = x^6 + 1$, calculate the value of $f(x_0)$ when $x = x_0$ using the Horner's method (also known as Qin Jiushao algorithm) and determine the number of times the operations of exponentiation, multiplication, and addition are required.

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