
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
Given a rectangular grid of cells, it is known that there are:

- exactly 940 ways to cut out a $1 \times 2$ rectangle along the grid lines;
- exactly 894 ways to cut out a $1 \times 3$ rectangle along the grid lines.

How many ways are there to cut out a $1 \times 5$ rectangle along the grid lines?

Both vertical and horizontal orientations of the rectangles are considered when counting the number of ways to cut them out.

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