
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
Determine the absolute value of the sum \[ \lfloor 2013\sin{0^\circ} \rfloor + \lfloor 2013\sin{1^\circ} \rfloor + \cdots + \lfloor 2013\sin{359^\circ} \rfloor, \] where  $\lfloor x \rfloor$  denotes the greatest integer less than or equal to  $x$ .

(You may use the fact that   $\sin{n^\circ}$  is irrational for positive integers  $n$  not divisible by  $30$ .)

*Ray Li*

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