
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
Let $AB$ be a diameter of a circle centered at $O$. Let $F$ be another point on the circle such that $AF$ is not a diameter, and $E$ is a different point on the circle such that it is neither $A$ nor $B$. The tangent at $B$, the tangent at $E$, and the tangent at $F$ intersect at points $C$, $D$, and $G$, respectively such that $BT$ (tangent at $B$) intersects with $FT$ (tangent at $F$) at $C$ and also $ET$ (tangent at $E$) intersects $FT$ at $D$ while $BT$ intersects $ET$ at $G$. Given $\angle BAF = 15^\circ$ and $\angle BAE = 43^\circ$, find $\angle CGD$, in degrees.

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