
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
Xiaoming and Xiaoqiang are playing a number game. Xiaoming chooses a number $x$ (between 0 and 9) and says, "I am thinking of a three-digit number (the hundreds digit can be 0). This three-digit number has $x$ as the hundreds digit, 3 as the tens digit, and it is divisible by 11. Please find the units digit of this three-digit number." Xiaoqiang is very happy because he knows the rule for numbers divisible by 11. However, after thinking, he realizes that no such three-digit number exists. What is $x$?

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