
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
The line segment connecting $(-3,5)$ to $(4,15)$ can be parameterized by the equations
\[
x = at + b, \quad y = ct + d,
\] where $-1 \le t \le 2,$ and $t = -1$ corresponds to the point $(-3,5).$ Find $a^2 + b^2 + c^2 + d^2.$

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