
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 degree of the polynomial 
\[ (x^5 + bx^8 + cx^2 + d)(x^4 + ex^3 + fy^2)(x + g) \]
where $b, c, d, e, f, g$ are all nonzero constants and $x$, $y$ are variables.

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