
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
What is the largest possible area of a rectangle whose vertices' coordinates satisfy the equation

\[ |y+1|\left(y^{2}+2y+28\right) + |x-2| = 9\left(y^{2}+2y+4\right) \]

with sides parallel to the coordinate axes?

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