
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
Let sets $P=\{b, 1\}$ and $Q=\{c, 1, 2\}$, with $P \subseteq Q$. If $b, c \in \{2, 3, 4, 5, 6\}$,
(1) Find the probability that $b=c$;
(2) Find the probability that the equation $x^2+bx+c=0$ has real roots.

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