
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
Nine fair coins are flipped independently and placed in the cells of a 3 by 3 square grid. Let \( p \) be the probability that no row has all its coins showing heads and no column has all its coins showing tails. If \( p = \frac{a}{b} \) for relatively prime positive integers \( a \) and \( b \), compute \( 100a + b \).

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