
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 comet orbits the Earth along a parabolic trajectory, with the Earth exactly at the focus of this parabola. When the comet is $d$ (in ten thousand kilometers) away from the Earth, the angle between the line through the Earth and the comet and the axis of the parabola is $60^{\circ}$. Find the shortest distance between the comet and the Earth.

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