
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 Cartesian coordinate system xOy, a line $l$ passes through point $P(0, \sqrt{3})$ with an angle of inclination $α$. Establish a polar coordinate system with O as the pole and the non-negative semi-axis of the x-axis as the polar axis. The polar equation of circle C is $ρ^{2}-4ρ\cos(θ- \frac {π}{3})-1=0$.

1. Find the parametric equation of line $l$ and the standard equation of circle C.
2. If line $l$ intersects with circle C at points M and N such that $|PM| - |PN| = \sqrt{2}$, find the value of the angle of inclination $α$.

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