
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
When using the Horner's method to calculate the value of the polynomial $f(x) = 9x^6 + 12x^5 + 7x^4 + 54x^3 + 34x^2 + 9x + 1$, the number of multiplication operations required is ______ times, and the number of addition operations required is ______ times.

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