
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
In parallelogram \(\mathrm{ABCD}\), the height \(\mathrm{BE}=3\), and the ratio \(\mathrm{AE}: \mathrm{ED}=1:4\). The side \(\mathrm{BC}=5\). On line segments \(\mathrm{BE}\) and \(\mathrm{BC}\), points \(\mathrm{G}\) and \(\mathrm{F}\) are marked respectively, such that \(\mathrm{BG}: \mathrm{GE}=1:2\) and \(\mathrm{BF}: \mathrm{FC}=3:2\). Determine the measure in degrees of angle \(\mathrm{FDG}\).

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