
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
For how many positive integers  $n$  less than or equal to  $1000$  is \[(\sin t + i \cos t)^n=\sin nt + i \cos nt\] true for all real  $t$ ?

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