
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
A bag contains 1 red ball and 1 black ball, both of which appear identical. Balls are drawn randomly with replacement 3 times, with 1 ball drawn each time. If drawing a red ball scores 2 points and drawing a black ball scores 1 point, calculate the probability that the total score after 3 draws is 5.

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