
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
If the proposition holds true when $n=k$ ($k \in \mathbb{N}^*$), then deduce the condition for the validity of the proposition when $n=k+1$. Given that the proposition does not hold true when $n=5$, conclude the validity of the proposition when $n=6$.

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