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

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