
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
Two (not necessarily different) numbers are chosen independently and at random from  $\{1, 2, 3, \dots, 10\}$ . On average, what is the product of the two integers? (Compute the expected product. That is, if you do this over and over again, what will the product of the integers be on average?)

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