
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
A positive integer $n$ is less than $50$ and satisfies the equation $[\frac{n}{2}]+[\frac{n}{3}]+[\frac{n}{6}]=n$, where $\left[x\right]$ represents the greatest integer not exceeding $x$. Find the number of positive integers that satisfy the equation.

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