
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
For the elective course "Coordinate System and Parametric Equations," determine the length of the chord cut by the line
$$
\begin{cases}
x=1+4t,
\\
y=-1-3t
\end{cases}
\quad (t \text{ is a parameter})
$$
from the curve
$$
\rho = \sqrt{2}\cos\left(\theta + \frac{\pi}{4}\right).
$$

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