
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
Marisa has two identical cubical dice labeled with the numbers  $\{1, 2, 3, 4, 5, 6\}$ . However, the two dice are not fair, meaning that they can land on each face with different probability. Marisa rolls the two dice and calculates their sum. Given that the sum is  $2$  with probability  $0.04$ , and  $12$  with probability  $0.01$ , the maximum possible probability of the sum being  $7$  is  $p$ . Compute  $\lfloor 100p \rfloor$ .

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