
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
Upon seeing a fox several meters away, a dog started chasing it down a straight countryside road. The dog's jump is $23\%$ longer than the fox's jump. There is a time interval during which both the fox and the dog make an integer number of jumps, and during this interval, the dog consistently manages to make $t\%$ fewer jumps than the fox, where $t$ is an integer. Assuming that all jumps are the same for both the dog and the fox, find the minimum value of $t$ at which the fox can escape from the dog.

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