
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
Nyusha has 2022 coins, and Barash has 2023. Nyusha and Barash toss all their coins simultaneously and count how many heads each gets. The one who gets more heads wins, and in case of a tie, Nyusha wins. What is the probability that Nyusha wins?

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