
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
(I) A circle is given by the equation $x^{2}+y^{2}=1$. Keep the abscissa of each point on the circle unchanged and double the ordinate to obtain a curve C. Write the parametric equation of C.
(II) In polar coordinates, find the number of common points of the line $\rho\cos (θ- \frac {π}{4})= \sqrt {2}$ and the circle $\rho=2$.

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