
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 $\{a,b,c\}=\{1,2,3\}$, and three relations: $①a\neq 3$, $②b=3$, $③c\neq 1$. Only one of these relations is correct. Find the value of $100a+10b+c=\_\_\_\_\_\_.$

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