
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
One fair die is rolled; let \( a \) denote the number that comes up. We then roll \( a \) dice; let the sum of the resulting \( a \) numbers be \( b \). Finally, we roll \( b \) dice, and let \( c \) be the sum of the resulting \( b \) numbers. Find the expected (average) value of \( c \).

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