
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
Find the maximum value of the function
\[
y = \tan \left( x + \frac{3 \pi}{4} \right) - \tan \left( x + \frac{\pi}{3} \right) + \cos \left( x + \frac{\pi}{3} \right) + \sin \left( x + \frac{\pi}{4} \right)
\]
for \(-\frac{5 \pi}{12} \le x \le -\frac{\pi}{4}.\)

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