
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  $9\times 7$  rectangle is tiled with tiles of the two types: L-shaped tiles composed by three unit squares (can be rotated repeatedly with  $90^\circ$ ) and square tiles composed by four unit squares.
Let  $n\ge 0$  be the number of the  $2 \times 2 $  tiles which can be used in such a tiling. Find all the values of  $n$ .

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