
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 Jiangjin Experimental High School girls' volleyball match is about to kick off in the seventh week. The team led by teacher Liu Guixia from class 6 of senior year two and the team led by teacher Zou Linna from class 1 of senior year two plan to have a warm-up match in the sixth week. The match adopts a best-of-five sets format, with the agreement that the first team to win 3 sets wins the match, and the match ends immediately. Except for the fifth set where class 6 of senior year two has a winning probability of $$\frac {1}{2}$$, the winning probability for class 6 of senior year two in each of the other sets is $$\frac {2}{3}$$. Assuming the results of each set are independent of each other, the probability of class 6 of senior year two winning by 3:0 is \_\_\_\_\_\_.

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