
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 points $(1,3,6)$ and $(6,-2,12)$ in 3D space can be parameterized by:
\begin{align*}
x &= at + b, \\
y &= ct + d, \\
z &= et + f,
\end{align*}
where $0 \le t \le 1,$ and $t = 0$ corresponds to the point $(1,3,6)$. Find the sum $a^2 + b^2 + c^2 + d^2 + e^2 + f^2$.

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