
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 sides of a triangle form an arithmetic sequence with a common difference of \(d\), and the area of the triangle is \(S\). Find the lengths of the sides and the angles of the triangle. Additionally, solve the problem for the specific case where \(d=1\) and \(S=6\).

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