
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
An equilateral triangle $ABC$ and rectangle $BCFG$ share a common vertex $B$ and side $BC$. Specifically, $BC = BG$. If the measure of angle $GBC$ is $80^\circ$, find the measure of angle $CAD$.

[asy]
size(70);
draw((0,0)--(20,0)--(20,10)--(0,10)--cycle);
draw((0,10)--(10,37.3)--(20,10));
draw((10,37.3)--(20,0));
label("$A$", (10,37.3), N);
label("$B$", (0,10), W);
label("$C$", (20,10), E);
label("$F$", (20,0), E);
label("$G$", (0,0), W);
[/asy]

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