
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 the equations
\[(x,y) = (3\cos t - 2\sin t, 5\sin t).\] 
Find the coefficients $a$, $b$, and $c$ so that the graph of the curve can be expressed in the form 
\[ax^2 + bxy + cy^2 = 9.\]

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