
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
Find the coordinates of point \( A \), which is equidistant from points \( B \) and \( C \).

\[ A(x; 0; 0) \]
\[ B(4; 6; 8) \]
\[ C(2; 4; 6) \]

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