
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
Find the smallest positive integer $t$ with the following property: when each small square in a $100 \times 100$ grid is colored in such a way that no color appears in more than 104 small squares, there exists a $1 \times t$ or $t \times 1$ rectangle containing at least three different colors in its $t$ small squares.

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