
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
From village $C$, a car departs at 7:58 AM, traveling eastward on a straight road toward village $B$ at a speed of $60 \text{ km/h}$. At 8:00 AM, a cyclist leaves the same village, traveling northward on a straight road toward village $A$, which is $10 \text{ km}$ away, at a speed of $18 \text{ km/h}$. A pedestrian had already left village $A$ at 6:44 AM, walking toward village $B$ along the straight road $A B$ at a speed of $6 \text{ km/h}$. The roads $A B$ and $A C$ form an angle of $60^{\circ}$. When will the cyclist be equidistant from both the car and the pedestrian in a straight line?

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