
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 greatest common divisor of the following pairs of numbers: $A$ and $C$, and $B$ and $C$.

$$
\begin{aligned}
& A=177^{5}+30621 \cdot 173^{3}-173^{5} \\
& B=173^{5}+30621 \cdot 177^{3}-177^{5} \\
& C=173^{4}+30621^{2}+177^{4}
\end{aligned}
$$

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