
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
Use the "Method of Mutual Subtraction" to find the greatest common divisor (GCD) of the two numbers in (1); use the "Euclidean Algorithm" to find the GCD of the two numbers in (2). Use the Horner's method to calculate the value of the function $f(x) = x^5 + x^3 + x^2 + x + 1$ when $x = 3$.

(1) 72, 168;  
(2) 98, 280.

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