
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
On April 1st, a class was practicing algebraic transformations in their math lesson. The exercise required simplifying the following expression:

$$
\frac{(x+2)^{3}+(y+x)^{3}}{(x+2)^{3}-(y-2)^{3}}
$$

A student named Ági, who is the best in the class at math, jokingly suggested that if the denominator is not zero, we could "simplify" using the cube exponents, resulting in:

$$
\frac{x+2+y+x}{x+2-(y-2)}=\frac{2 x+y+2}{x-y+4}
$$

Determine whether the final result is correct.

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