
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
A weather forecast predicts that for one week (Monday to Sunday), the probability forecasts for each day are as follows: $20\%$ chance of no rain, $30\%$ chance of getting 2 inches of rain, and $50\%$ chance of getting 8 inches of rain. What is the expected value of the total number of inches of rain which will fall for the entire week?

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