
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
If in a trapezoid \(AB = a\), \(BC = b\), \(CD = c\), \(DA = d\), then:

1. \(a = d \cos \alpha + b \cos \beta - c \cos (\beta + \gamma) = d \cos \alpha + b \cos \beta - c \cos (\alpha + \delta)\)

2. \(a \sin \alpha = c \sin \delta + b \sin (\alpha + \beta)\)

3. \(a \sin \beta = c \sin \gamma + d \sin (\alpha + \beta)\)

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