
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 local meteorological service forecasts the following for the next week, from Monday to Sunday:
- A $30\%$ chance of sun with no rain,
- A $35\%$ chance of getting 3 inches of rain,
- A $35\%$ chance of getting 8 inches of rain.

Calculate the expected value of the total rainfall amount for the upcoming week. Report your answer as a decimal rounded to the nearest tenth.

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