
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
The school plans to organize a movie viewing for the students either on January 4th or January 10th. After finalizing the date, the teacher informs the class leader. However, due to the similarity in pronunciation between "four" and "ten," there is a 10% chance that the class leader hears it incorrectly (mistaking 4 for 10 or 10 for 4). The class leader then informs Xiaoming, who also has a 10% chance of hearing it incorrectly. What is the probability that Xiaoming correctly believes the movie date?

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