
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
In recent years, China's scientific and technological achievements have been remarkable. The Beidou-3 global satellite navigation system has been operational for many years. The Beidou-3 global satellite navigation system consists of 24 medium Earth orbit satellites, 3 geostationary Earth orbit satellites, and 3 inclined geosynchronous orbit satellites, totaling 30 satellites. The global positioning accuracy of the Beidou-3 global satellite navigation system is better than 10 meters, and the measured navigation positioning accuracy is 2 to 3 meters. The global service availability is 99%, with better performance in the Asia-Pacific region. Now, two satellites are selected for signal analysis from the geostationary Earth orbit satellites and inclined geosynchronous orbit satellites.<br/>$(1)$ Find the probability of selecting exactly one geostationary Earth orbit satellite and one inclined geosynchronous orbit satellite;<br/>$(2)$ Find the probability of selecting at least one inclined geosynchronous orbit satellite.

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