
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
In the rectangular coordinate system on a plane, with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, a coordinate system is established. Given that the polar coordinate equation of curve $C\_1$ is $ρ=4\cos θ$. The parametric equation of curve $C\_2$ is $\begin{cases} & x=4t^{2} \ \\ & y=4t \ \end{cases}(t\text{ is the parameter})$. Find the length of the chord formed by the intersection of curve $C\_1$ and the line passing through the focus of curve $C\_2$ with a slope of $2$.

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