
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 maximum value of 
\[y = \sin\left(x + \frac{\pi}{4}\right) + \sin\left(x + \frac{\pi}{3}\right) \cdot \cos\left(x + \frac{\pi}{6}\right)\] 
for \( -\frac{\pi}{4} \leq x \leq \frac{\pi}{12} \).

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