
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
Find all values of $r$ and $s$ such that $\lfloor r \rfloor + r + \lceil s \rceil = 10.7$. Assume $r$ and $s$ are real numbers and $\lfloor r \rfloor$ and $\lceil s \rceil$ are their respective floor and ceiling values.

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