
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 xOy, the parametric equations of the circle C are given by
\[
\begin{cases}
x = a + \cos \theta, \\
y = \sin \theta,
\end{cases}
\]
where θ is the parameter. Using the origin as the pole and the non-negative half of the x-axis as the polar axis, establish a polar coordinate system. The polar equation of the line l is ρ sin(θ - π/4) = √2/2. If the line l is tangent to the circle C, find the number of possible values of the real number a.

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