
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 $A$ equidistant from points $B$ and $C$.

$A(x ; 0 ; 0)$

$B(-2 ; 0 ; 6)$

$C(0 ;-2 ;-4)$

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