
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
"The Comprehensive Collection of Mathematical Algorithms" is an important ancient Chinese mathematical work. It records: I asked Li Sangong, who owns a store, all the guests came to the store. If seven guests stay in each room, there will be seven guests left without a room. If nine guests stay in each room, there will be one room empty. The question is: if there are several people staying in the store, and if each room accommodates 7 people, then 7 people will be left without a room. If each room accommodates 9 people, then one room will be empty. Let the total number of rooms in the store be $x$. What is the value of $x$?

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