
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
According to the national deployment, in 2022, China's space station "Tiangong" will officially complete its in-orbit construction task and become a national-level space laboratory with long-term human care to support large-scale, interdisciplinary space science experiments. To popularize knowledge related to the space station, a department organized a 3D simulation programming challenge based on the space station construction process. It consists of 10 independent programming questions including space launch, custom roaming, full-size solar energy, space transportation, etc. The rule is: writing a program that can run correctly is considered a correct program. Each participant randomly selects 3 out of the 10 different questions to program. After completing all tasks, they submit to the judges for testing. If 2 or more programs are correct, the participant successfully completes the challenge. It is known that out of the 10 programs, person A can only correctly complete 6 of them, and person B has a probability of $\frac{3}{5}$ of correctly completing each program. Each participant's programming does not affect each other.<br/>$(1)$ Find the probability of person B successfully completing the challenge;<br/>$(2)$ Find the distribution and mathematical expectation of the number $X$ of correct programs written by person A, and determine who is more likely to successfully complete the challenge, person A or person B.

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