
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 room temperature \( T \) (in degrees Celsius) as a function of time \( t \) (in hours) is given by: 
\[ T = a \sin t + b \cos t, \quad t \in (0, +\infty) \]
where \( a \) and \( b \) are positive real numbers. If the maximum temperature difference in the room is 10 degrees Celsius, what is the maximum value of \( a + b \)?

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