
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 \( OABC \), the vertices are given as \( O(0, 0) \), \( A(3, 6) \), and \( B(8, 6) \). Find the ratio of the lengths of the diagonals \( OB \) and \( AC \), and also determine the equations of the sides of the parallelogram and the diagonal \( AC \).

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