
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
Given the function \( f(x)=\sin \omega x+\cos \omega x \) where \( \omega > 0 \) and \( x \in \mathbb{R} \), if the function \( f(x) \) is monotonically increasing on the interval \( (-\omega, \omega) \) and the graph of the function \( y=f(x) \) is symmetric with respect to the line \( x=\omega \), determine the value of \( \omega \).

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