
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
Determine the value of the following sum:

$$
\log _{3}\left(1-\frac{1}{15}\right)+\log _{3}\left(1-\frac{1}{14}\right)+\log _{3}\left(1-\frac{1}{13}\right)+\cdots+\log _{3}\left(1-\frac{1}{8}\right)+\log _{3}\left(1-\frac{1}{7}\right)+\log _{3}\left(1-\frac{1}{6}\right)
$$

(Note that the sum includes a total of 10 terms.)

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