
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
Suppose a hotel has a total of 30 rooms, numbered from 1 to 30. Now, it is required to engrave numbers on each room's key so that the staff can easily identify which room the key belongs to, while making it difficult for outsiders to guess. There is a method of encoding: engrave two numbers on each key, where the number on the left is the remainder when the original room number is divided by 5, and the number on the right is the remainder when the original room number is divided by 7. Then, the numbers engraved on the key for room 36 should correspond to room number $\boxed{\text{13}}$.

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