
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 box contains three cards, labeled with the numbers $1$, $2$, and $3$ respectively. The cards are identical in all aspects except for the numbers. Draw three times randomly with replacement, each time drawing one card, and record the numbers on the drawn cards as $a$, $b$, and $c$.

1. Find the probability that the drawn numbers satisfy $a + b = c$.
2. Find the probability that the drawn numbers $a$, $b$, and $c$ are not all the same.

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

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