
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 robotic vacuum cleaner is programmed to move on the floor according to the following equations:

\[
\left\{
\begin{array}{l}
x = (t-6)^{2} \quad \text{where} \quad y = 0 \quad \text{for} \quad 0 \leq t \leq 7 \\
y = (t-7)^{2} \quad \text{for} \quad t \geq 7
\end{array}
\right.
\]

Here, the axes are chosen parallel to the walls. Time $t$ is measured in minutes, and the coordinates are in meters.

Find the path traveled by the robot in the first 7 minutes and the magnitude of the change in the velocity vector in the eighth minute.

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