
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
Determine the smallest constant $D$ such that for all real numbers $\theta$,
\[
\sin^2 \theta + \cos^2 \theta + 1 \geq D (\sin \theta + \cos \theta)
\]

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