
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
How many positive integer solutions does the equation have   $$ \left\lfloor\frac{x}{10}\right\rfloor= \left\lfloor\frac{x}{11}\right\rfloor + 1? $$  ( $\lfloor x \rfloor$  denotes the integer part of  $x$ ,  for example  $\lfloor 2\rfloor = 2$ ,  $\lfloor \pi\rfloor = 3$ ,  $\lfloor \sqrt2 \rfloor =1$ )

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