
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
Two plane equations in normal form are given. How can you derive the equation of the set of points that are equidistant from both planes? (This set is the union of the bisector planes of the dihedral angles between the given planes.)

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