
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
There are  $ 2010 $  people sitting around a round table. First, we give one person  $ x $  a candy. Next, we give candies to  $1$  st person,  $1+2$  th person,  $ 1+2+3$  th person,  $\cdots$  , and  $1+2+\cdots + 2009 $  th person clockwise from  $ x $ . Find the number of people who get at least one candy.

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