
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 line $l$: 
$$
\begin{cases} 
x=1+t\cos\alpha \\
y=t\sin\alpha 
\end{cases}
$$
(where $t$ is a parameter, $\alpha$ is the angle of inclination). Taking the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The polar equation of curve $C$ is $\rho= \frac {\cos\theta}{\sin^{2}\theta}$.  
(1) Find the rectangular coordinate equation of $C$ and the rectangular coordinates of the focus $F$ of $C$;  
(2) Given point $P(1,0)$, if line $l$ intersects $C$ at points $A$ and $B$, and $\frac {1}{|PA|}+ \frac {1}{|PB|}=2$, find the area of $\triangle FAB$.

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