
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
A curve is described parametrically by:
\[(x, y) = (3 \sin t + \cos t, 3 \cos t)\]
Calculate the constants such that the graph of the curve can be expressed in the form 
\[ax^2 + bxy + cy^2 = 3.\]
Find the ordered triple \((a, b, c)\).

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