
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 that \( A, B, D, F \), and \( G \) lie on a vertical line, \( \triangle B C D \) is right-angled at \( C \), and \( \triangle D E F \) is right-angled at \( E \), with \( \angle A B C = x^{\circ} \), \( \angle C D E = 80^{\circ} \), and \( \angle E F G = y^{\circ} \), find the value of \( x + y \).

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