
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
A line is given by the parametric equations $\begin{cases} x = 1 + \frac{1}{2}t, \\ y = -5 + \frac{\sqrt{3}}{2}t \end{cases}$ where $t$ is the parameter. Another line is defined by the equation $x - y - 2\sqrt{3} = 0$. Find the distance from the point of intersection $P$ of these two lines to the point $P_0(1,-5)$.

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