
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 $2 \times 5$ grid has one of its four corner cells removed. The remaining 9 cells form eight different shapes, all of which are referred to as "flags". Given a fixed $9 \times 18$ grid, how many different ways are there to completely cover it using 18 of these flags? Explain your reasoning.

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