
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
Given the digits  $1$  through  $7$ , one can form  $7!=5040$  numbers by forming different permutations of the  $7$  digits (for example,  $1234567$  and  $6321475$  are two such permutations).  If the  $5040$  numbers are then placed in ascending order, what is the  $2013^{\text{th}}$  number?

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