
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 coin and a die are thrown simultaneously. If the coin shows heads, it is counted as 2, and if it shows tails, it is counted as 1. The product of this number and the die's result is denoted as \( x \) (for example, if the coin shows heads and the die shows 3, then \( x = 2 \times 3 = 6 \)). What is the expected value of \( x \)?

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