
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 a curve C with the polar coordinate equation ρ$^2$cos2θ=a$^2$ (where a∈R and a is a constant), and a line l with the parameter equation x=2+$\frac{\sqrt{3}}{2}$t (t is the parameter) that passes through point P(2,1) with a slope angle of 30°.

1. Find the Cartesian equation of curve C and the parameter equation of line l.
2. If line l intersects curve C at points A and B (with point P between A and B) and |PA|•|PB|=2, find the values of a and ||PA|-|PB||.

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