
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 sequence of rectangles is created, where each rectangle is composed of tiles arranged such that the width of each rectangle in tiles is double the position in the sequence, and the height is the position itself. Calculate the difference in the number of tiles required for the ninth and eighth rectangles.

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