
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 a proposition related to the positive integer $n$, if the proposition holds true when $n=k$ ($k\in\mathbb{N}_{+}$), then it can be deduced that the proposition also holds true when $n=k+1$. It is known that the proposition does not hold true when $n=7$. Determine whether the proposition holds true when $n=6$.

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