
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
\[
(x,y) = (3 \cos t + 2 \sin t, 5 \sin t).
\]
Determine if this parametrization allows the curve to be expressed in the form
\[
Ax^2 + Bxy + Cy^2 = 1.
\]
If so, find the ordered triple $(A, B, C)$.

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