
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 length of the chord intercepted by the curve $\rho =\sqrt{2}\cos (\theta +\frac{\pi }{4})$ from the line given by the parametric equations $\begin{cases} x=1+\dfrac{4}{5}t \\ y=-1-\dfrac{3}{5}t \end{cases}$ with $t$ as the parameter.

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