
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
Let \( P \) and \( Q \) be points on the coordinate plane with coordinates \( (2t+3, t-5) \) and \( (t-1, 2t+4) \), respectively. The square of the distance between the midpoint of \( \overline{PQ} \) and point \( P \) is equal to \( \frac{3t^2}{4} \). Find the value of \( t \).

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