
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
Given the set $\{a, b, c\} = \{0, 1, 2\}$, and the following three conditions: ① $a \neq 2$; ② $b = 2$; ③ $c \neq 0$ are correct for only one of them, then $10a + 2b + c$ equals $\boxed{?}$.

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