
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

There are 100 points $P_{1}, P_{2}, \cdots, P_{100}$ in order on a circle (where $P_{100}$ and $P_{1}$ are adjacent). Each point $P_{1}, P_{2}, \cdots, P_{100}$ must be colored with one of 5 colors, and each color must be used at least once. For any such coloring, there must exist $t$ consecutive points among $P_{1}, P_{2}, \cdots, P_{100}$ containing at least 3 different colors. Find the minimum value of $t$.

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