
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
If you alphabetize all of the distinguishable rearrangements of the letters in the word **PURPLE**, find the number  $n$  such that the word **PURPLE**is the  $n$ th item in the list.

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