
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
One fine summer day, François was looking for Béatrice in Cabourg. Where could she be? Perhaps on the beach (one chance in two) or on the tennis court (one chance in four), it could be that she is in the cafe (also one chance in four). If Béatrice is on the beach, which is large and crowded, François has a one in two chance of not finding her. If she is on one of the courts, there is another one in three chance of missing her, but if she went to the cafe, François will definitely find her: he knows which cafe Béatrice usually enjoys her ice cream. François visited all three possible meeting places but still did not find Béatrice.

What is the probability that Béatrice was on the beach, assuming she did not change locations while François was searching for her?

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