
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
Parameterize the line segment connecting points $(1,3)$ and $(4,9)$ with equations $x = at + b$, $y = ct + d$ where $t = 0$ corresponds to $(1,3)$ and $t = 1$ corresponds to $(4,9)$. Find $a^2 + b^2 + c^2 + d^2$.

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