
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
In the configuration below, $\phi$ is measured in radians, $C$ is the center of the circle, $BCD$ and $ACE$ are line segments, and $AB$ is tangent to the circle at $A$.
[asy] defaultpen(fontsize(10pt)+linewidth(.8pt)); pair A=(0,-1), E=(0,1), C=(0,0), D=dir(20), F=dir(160), B=(-1/sin(20*pi/180))*dir(20); fill(Arc((0,0),1,20,90)--C--D--cycle,mediumgray); fill(Arc((0,0),1,160,270)--B--F--cycle,mediumgray); draw(unitcircle); draw(A--B--D^^A--E); label("$A$",A,S); label("$B$",B,W); label("$C$",C,SE); label("$\phi$",C,SW); label("$D$",D,NE); label("$E$",E,N); [/asy]
What is the necessary and sufficient condition for the equality of the two shaded areas, given $0 < \phi < \frac{\pi}{2}$?

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