
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
Two cards are drawn at random from a pack and not replaced. Find the probability $\frac{1}{a}$ that both cards are hearts.

If there are $b$ ways of choosing 15 people from ' $a$ ' people, find $b$.

If $c$ signals can be made with $\frac{b}{2 a}$ flags of different colours by raising at least one of the flags, without considering the arrangement of colours, find $c$.

There are $c$ balls in a bag, of which 3 are red. What is the probability of drawing a red ball?

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