
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
Starting with a  $5 \times 5$  grid, choose a  $4 \times 4$  square in it. Then, choose a  $3 \times 3$  square in the  $4 \times 4$  square, and a  $2 \times 2$  square in the  $3 \times 3$  square, and a  $1 \times 1$  square in the  $2 \times 2$  square. Assuming all squares chosen are made of unit squares inside the grid. In how many ways can the squares be chosen so that the final  $1 \times 1$  square is the center of the original  $5 \times 5$  grid?

*Proposed by Nancy Kuang*

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