
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
Determine the number of multiplications required to calculate the value of the function $f(x) = 5x^6 - 7x^5 + 2x^4 - 8x^3 + 3x^2 - 9x + 1$ at $x = x$ using Horner's method, as opposed to 21 multiplications needed when using the direct method.

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