
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
Toss a die 6 times, and let the number obtained on the $i$-th toss be $a_{i}$. If there exists a positive integer $k$ such that $\sum_{i=1}^{k} a_{i}=6$, what is the probability $p=\frac{n}{m}$, where $m$ and $n$ are coprime positive integers. Find the value of $\log _{6} m - \log _{7} n$.

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