
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
A large rectangle has side lengths of $(2x+14)$ and $(2x+10)$. Inside this rectangle, there is a rectangular hole whose dimensions are linked by the equation $(y+1) = (x-2)$, with $y$ being the shorter side of the hole and $x$ the longer side. If the longer side of the hole is $(2y+3)$, determine the area of the large rectangle excluding the hole. Express your answer as a polynomial in $x$.

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