
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
(1) Use the Euclidean algorithm to find the greatest common divisor (GCD) of 117 and 182.

(2) Use Horner's method to evaluate the polynomial $f(x) = 1−9x+8x^{2}−4x^{4}+5x^{5}+3x^{6}$ at $x = −1$.

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