
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
Let  $a$  be a positive integer.

How many non-negative integer solutions x does the equation

 $\lfloor \frac{x}{a}\rfloor = \lfloor \frac{x}{a+1}\rfloor$ 

have?

 $\lfloor ~ \rfloor$  ---> [Floor Function](http://en.wikipedia.org/wiki/Floor_function).

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