
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
Let $A$ and $B$ be two assertions. Show the following equivalences:

1. $\operatorname{non}(A$ and $B) \Longleftrightarrow($ not $A)$ or $($ not $B)$
2. $\operatorname{non}(A$ or $B) \Longleftrightarrow($ not $A)$ and $($ not $B)$.

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