
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 cat runs counterclockwise across eight squares, moving to a neighboring square every second. A mouse runs clockwise around the perimeter of a large square, moving to the next segment every second (see diagram). The picture shows the starting position from left to right, and then positions 1, 2, and 3 seconds after the start respectively. Where will the cat and mouse be 2023 seconds after the start? (20 points)

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