
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
For any real number $x$, the symbol $[x]$ represents the largest integer not greater than $x$. For example, $[2]=2$, $[2.1]=2$, $[-2.2]=-3$. The function $y=[x]$ is called the "floor function", which has wide applications in mathematics and practical production. Then, the value of $[\log _{3}1]+[\log _{3}2]+[\log _{3}3]+…+[\log _{3}11]$ is \_\_\_\_\_\_.

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