
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
An airline company is planning to introduce a network of connections between the ten different airports of Sawubonia. The airports are ranked by priority from first to last (with no ties). We call such a network *feasible* if it satisfies the following conditions:



- All connections operate in both directions
- If there is a direct connection between two airports A and B, and C has higher priority than B, then there must also be a direct connection between A and C.


Some of the airports may not be served, and even the empty network (no connections at all) is allowed. How many feasible networks are there?

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