
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
Find the parameters \(a, b, c, d\) for the line segment connecting the points \((1, -3)\) and \((-4, 9)\) such that it can be described by the equations:
\begin{align*}
x &= at + b, \\
y &= ct + d,
\end{align*}
where \(0 \le t \le 1\), and \(t = 0\) corresponds to the point \((1, -3)\). Calculate \(a^2 + b^2 + c^2 + d^2.\)

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