
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 deck of cards contains only red and black cards. Initially, the probability of drawing a red card is $\frac{1}{5}$. When $6$ black cards are added to the deck, the probability of choosing a red card becomes $\frac{1}{7}$. Let $r$ denote the number of red cards originally in the deck. Find the value of $r$.

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