
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 $3\times 4$ rectangle and a $4\times 5$ rectangle are to be placed inside a square. The rectangles should not overlap at any interior point, and the sides of the square are parallel to at least one side of each rectangle. Additionally, one rectangle must be rotated 90 degrees relative to its original orientation. What is the smallest possible area of the square?

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