
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 equation of line $l$ is given by
$$
\begin{cases}
x=t \\
y=1+kt
\end{cases}
$$
(where $t$ is the parameter). Taking the origin $O$ as the pole and the positive half of the x-axis as the polar axis, with unit length unchanged, a polar coordinate system is established. The polar equation of curve $C$ is $\rho \sin^2\theta = 4\cos\theta$. If line $l$ is tangent to curve $C$, then the value of the real number $k$ is ______.

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