
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
As shown in the image, there is a convex-shaped paper made up of four $1 \times 1$ small squares and a $5 \times 6$ grid paper. The convex-shaped paper needs to be pasted onto the grid paper such that each small square of the convex-shaped paper overlaps with a small square on the grid paper. How many distinct shapes can be formed? (Two shapes that are identical after rotation are considered the same shape.)

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