
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
Given the equation of a line $ax + by + c = 0 (ab \neq 0)$, find the condition that coefficients $a$, $b$, and $c$ must satisfy for the line to have equal intercepts on both coordinate axes.

A) $a = b$
B) $|a| = |b|$
C) $a = b$ and $c = 0$
D) $c = 0$ or $c \neq 0$ and $a = b$

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