
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
Given the polar equation of circle \(C\) is \(\rho = 4\cos\theta\), using the pole as the origin of the Cartesian coordinate system and the polar axis as the positive half of the \(x\)-axis, we establish a Cartesian coordinate system. The parametric equation of line \(l\) is:
$$
\begin{cases} 
x = \frac{\sqrt{2}}{2}t + m \\ 
y = \frac{\sqrt{2}}{2}t 
\end{cases}
$$
(\(t\) is the parameter). If line \(l\) is tangent to circle \(C\), find the value of the real number \(m\).

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