
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 sequence $\{x_n\}$ with a fixed number of terms $p$ ($p \in \mathbb{N}^*$, $p > 2$), where $x_i \in \{u, v\}$ ($i=1, 2, \ldots, p$) and the sequence is a "3-order $\Gamma$ sequence", calculate the minimum value of $p$.

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