
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
An isosceles triangle with base angles of 45 degrees each is divided into sections by its altitudes and a median from the vertex opposite the base, as shown. Three of these sections are shaded. What is the probability that the tip of a spinner, spinning and landing randomly on the triangle, will rest in a shaded area? Express your answer as a common fraction.

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