
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
How many of the numbers from $100$ to $999$ have three different digits which:
1. Are in strictly increasing order.
2. Are in strictly decreasing order.
Furthermore, no digit used in either set can repeat across the two groups.
A) 168
B) 336
C) 840
D) 1680
E) 2016

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