
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
Given the parametric equations of curve $C\_1$ as $ \begin{cases} x=2\cos θ \
y= \sqrt {3}\sin θ\end{cases}$ (where $θ$ is the parameter), point $P(-1,0)$, and the polar coordinate equation of line $C\_2$ as $ρ\cos θ-ρ\sin θ+1=0$.

1. Write the Cartesian equation of curve $C\_1$ and the parametric equations of line $C\_2$.
2. If curve $C\_1$ intersects line $C\_2$ at points $A$ and $B$, find $|PA|⋅|PB|$.

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