
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 `k` is an odd integer and `m/k` is defined as the integer closest to `m/k` for any integer `m`, determine the minimum possible value of `P(k)`, where `P(k)` is the probability that `[n/k] + [150 - n/k] = [150/k]` holds for an integer `n` randomly chosen from the interval `1 ≤ n ≤ 75`.

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