
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
Given that there are 10 boxes of X-ray films with 5 boxes produced by Factory A, 3 boxes produced by Factory B, and 2 boxes produced by Factory C, with defective rates of $\frac{1}{10}$, $\frac{1}{15}$, and $\frac{1}{20}$ respectively, calculate the probability that a randomly selected X-ray film is defective.

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