
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
If for any \(\theta \in \left[0, \frac{\pi}{2}\right]\), the inequality 
\[ 
4 + 2 \sin \theta \cdot \cos \theta - a \sin \theta - a \cos \theta \leq 0 
\] 
always holds, then the minimum value of the real number \(a\) is \(\quad\).

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