
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
Two students, A and B, are playing a chess match using a "best of five" format (the first player to win three games wins the match). Based on their past performance, the probability of A winning each game is $p$ $(0 < p < 1)$, and the outcomes of each game are independent. If the probability of A winning with a score of $3:1$ is not higher than the probability of A winning with a score of $3:2$, then the possible range of values for $p$ is ______.

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