
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
The coefficient of $x^{4}y^{2}$ in the expansion of $(x^{2}-y+2)^{5}$ can be found using the binomial theorem. Using the formula for the coefficient of $x^{4}y^{2}$, $\binom{n}{k} \cdot a^{n-k} \cdot b^{k}$, where n is the exponent of the binomial raised to the power, k is the number of times b is raised to the power, a is the first term of the binomial, and b is the second term of the binomial, determine the coefficient of $x^{4}y^{2}$ in the expansion of $(x^{2}-y+2)^{5}$.

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