
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 equation of line $l_1$ is $x- \sqrt {2}y+1=0$, its inclination angle is $\alpha$. A line $l$ passes through the point $P(-\sqrt {2}, 2)$ with an inclination angle of $\beta$, and $\beta=2\alpha$.  
(1) Find the general form equation of line $l$;  
(2) The value of $\frac {\cos2\beta}{1+\cos2\beta-\sin2\beta}$.

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