
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
Equilateral triangle $ABC$ and rectangle $BCFG$ share a side $BC$, with rectangle lengths larger than widths as shown. What is the number of degrees in the measure of angle $CAG$?

[asy]
size(80);
draw((0,0)--(30,0)--(30,10)--(0,10)--cycle);
draw((0,10)--(15,28.6)--(30,10));
draw((15,28.6)--(30,0));
label("$A$",(15,28.6),N);
label("$B$",(0,10),W);
label("$C$",(30,10),E);
label("$G$",(30,0),E);
label("$F$",(0,0),W);
[/asy]

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