
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
We have that \( 2 \cdot f(x) + 5 \cdot g(x) = h(x) \) where \( f(x), g(x), \) and \( h(x) \) are all polynomials in \( x \). If the degree of \( f(x) \) is \( 7 \) and the degree of \( h(x) \) is \( 10 \), then what is the minimum possible degree of \( g(x) \)?

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