
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
An box contains three cards labeled with the numbers $1$, $2$, and $3$. These three cards are identical except for the numbers on them. The cards are randomly drawn with replacement three times, drawing one card each time. Let the numbers on the drawn cards be denoted as $a$, $b$, and $c$.

(1) Find the probability that the numbers on the drawn cards satisfy $a + b = c$.

(2) Find the probability that the numbers $a$, $b$, and $c$ on the drawn cards are not completely identical.

(Note: If three numbers $a$, $b$, $c$ satisfy $a\leq b\leq c$, then $b$ is called the median of these three numbers.)

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