
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
In a lottery event, there are six people, namely $a$, $b$, $c$, $d$, $e$, and $f$, who have the chance to draw lots. The rules are as follows: The organizer first randomly selects two people from the six to win the first prize, then randomly selects one person from the remaining four to win the second prize, and finally randomly selects one person from these four to win the third prize.

(1) Calculate the probability that $a$ wins the first prize;

(2) If $a$ and $b$ have won the first prize, calculate the probability that $c$ wins any prize.

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