
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
If all the terms of a polynomial have the same degree, then the polynomial is called a homogeneous polynomial. For example, $x^3 + 2xy^2 + 2xyz + y^3$ is a homogeneous polynomial of degree 3. If $x^{m+2}y^2 + 3xy^3z^2$ is a homogeneous polynomial, then $m$ equals to ____.

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