
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 points $A$ and $B$ be on the coordinate plane with coordinates $(2t-3, 0)$ and $(1, 2t+2)$, respectively. The square of the distance between the midpoint of $\overline{AB}$ and point $A$ is equal to $2t^2 + 3t$. What is the value of $t$?

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