
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 certain circuit switch, when closed, will cause either a red or green light to flash. It is known that the probability of a red light flashing after the switch is closed for the first time is $\frac{1}{2}$, and the probability of a red light flashing after the switch is closed twice is $\frac{1}{5}$. What is the probability that a red light will flash the second time the switch is closed, given that it flashed red the first time?

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