
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 conic section curve $C$: $ \begin{cases}x=2\cos α \\\\ y= \sqrt {3}\sin α\end{cases}(α$ is a parameter$) and the fixed point $A(0, \sqrt {3})$, $F_{1}$, $F_{2}$ are the left and right foci of the curve $C$, respectively.
1. Establish a coordinate system with the origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Find the polar coordinate equation of the line $AF_{2}$.
2. If $P$ is a moving point on the curve $C$, find the range of values for $| \overrightarrow{PF_{1}}|⋅| \overrightarrow{PF_{2}}|$.

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