
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
Given a right trapezoid $\mathrm{ABCE}$ with bases $\mathrm{BC}$ and $\mathrm{AE}$ measuring 3 and 4, respectively, and with the shorter leg $\mathrm{AB}$ equal to $\mathrm{BC}$. Point $\mathrm{D}$ is marked on $\mathrm{AE}$ such that $\mathrm{AD}: \mathrm{DE}=3: 1$; point $\mathrm{F}$ is marked on $\mathrm{AD}$ such that $\mathrm{AF}: \mathrm{FD}=2: 1$; and point $\mathrm{G}$ is marked on $\mathrm{BD}$ such that $\mathrm{BG}: \mathrm{GD}=1: 2$. Determine the degree measure of the angle $\mathrm{CFG}$.

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