
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 Cartesian coordinate system, the parametric equations of line \( l \) are given by 
$$
\begin{cases}
x = 6 + \frac{\sqrt{2}}{2}t, \\
y = \frac{\sqrt{2}}{2}t.
\end{cases}
$$
where \( t \) is the parameter. Now, establishing a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, the polar equation of curve \( C \) is 
$$
p = 6\cos θ.
$$

(I) Write down the standard (general) equation of line \( l \) and the Cartesian equation of curve \( C \).

(II) Through point \( M(-1,0) \) and parallel to line \( l \), line \( l_1 \) intersects curve \( C \) at points \( A \) and \( B \). Find the length of \( |AB| \).

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