
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 the Cartesian coordinate system \( xy \), the position of a moving point A is given by \( (2 - 3\sin\alpha, 3\cos\alpha - 2) \), where \( \alpha \in \mathbb{R} \). In the polar coordinate system, with the origin \( O \) as the pole and the positive \( x \)-axis as the polar axis, the equation of line \( C \) is \( \rho\cos(\theta - \frac{\pi}{4}) = a \).
(Ⅰ) Determine the shape of the trajectory of point A.
(Ⅱ) If line \( C \) has exactly one point in common with the trajectory of point A, find the value of the real number \( a \).

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