
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
Martha writes down a random mathematical expression consisting of 3 single-digit positive integers with an addition sign " $+$ " or a multiplication sign " $\times$ " between each pair of adjacent digits.  (For example, her expression could be  $4 + 3\times 3$ , with value 13.)  Each positive digit is equally likely, each arithmetic sign (" $+$ " or " $\times$ ") is equally likely, and all choices are independent.  What is the expected value (average value) of her expression?


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