
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
In the ancient Chinese mathematical text "The Mathematical Classic of Sunzi", there is a problem that goes: Three people share a carriage, leaving two carriages empty; when two people share a carriage, nine people are left walking. The question is: How many people and carriages are there? This question means that there are several people riding in carriages, with three people sharing one carriage, leaving $2$ carriages empty in the end. If every $2$ people share one carriage, there are $9$ people left without a carriage. The task is to find out how many people and carriages there are. If we assume there are $x$ carriages, we can set up the equation ______.

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