
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
Find the smallest integer solution of the equation

$$
\left\lfloor\frac{x}{8}\right\rfloor-\left\lfloor\frac{x}{40}\right\rfloor+\left\lfloor\frac{x}{240}\right\rfloor=210
$$

(If $x$ is a real number, $\lfloor x\rfloor$ is the floor of $x$, that is, the greatest integer less than or equal to $x$.)

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