
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, a polar coordinate system is established with the origin O as the pole and the positive half of the x-axis as the polar axis. The polar equation of curve C is $\rho \sin^2 \theta + 4\sin \theta - \rho = 0$. The line $l$ is given by the parametric equations $\begin{cases} x=2+t\cos \alpha \\ y=3+t\sin \alpha \end{cases}$ where \(t\) is a parameter. Line $l$ passed through the focus of curve C. Determine the value of $\tan \alpha$.

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