
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
Xiaoming needs to win 2 more rounds to ultimately win, while Xiaojie needs to win 3 more rounds to ultimately win. The probability of winning each round for both players is $\frac {1}{2}$. Determine the probability that Xiaoming wins 2 consecutive rounds and ultimately wins.

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