
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 $f(x) = A\sin\left(\frac{\pi}{4}x + \frac{\pi}{4}\right)$, where $x \in \mathbb{R}$, and $f(-2015) = 3$  
(1) Find the value of $A$.  
(2) Identify the intervals of monotonicity for the function $f(x)$ on the interval $x \in [0, 8]$. (The process is not required.)  
(3) If $f\left(\frac{4a}{\pi} - 1\right) + f\left(\frac{4a}{\pi} + 1\right) = \frac{3}{5}$, where $a \in [0, \pi]$, find $\cos 2a$.

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