
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 $BCGF$ are coplanar, with $BC = BF = 3x$ and $FG = 2x$. Determine the measure of angle $CAG$.

[asy]
size(110);
draw((0,0)--(60,0)--(60,40)--(0,40)--cycle);
draw((0,40)--(30,76.769)--(60,40));
draw((30,76.769)--(60,0));
label("$A$",(30,76.769),N);
label("$B$",(0,40),W);
label("$C$",(60,40),E);
label("$G$",(60,0),E);
label("$F$",(0,0),W);
[/asy]

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