
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
The digits \(1, 2, 3, 4, 5, 6\) are randomly chosen (without replacement) to form the three-digit numbers \(M = \overline{ABC}\) and \(N = \overline{DEF}\). For example, we could have \(M = 413\) and \(N = 256\). Find the expected value of \(M \cdot N\).

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