
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
The equation of the base line of a certain triangle is \( 55y + 18x - 256 = 0 \). The x-coordinates of its endpoints are \( x_{1} = 2 \) and \( x_{2} = 7.5 \). The coordinates of the centroid of the triangle are \( \alpha = 5 \) and \( \beta = 6 \). What are the lengths of the sides and the angles?

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