
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 $f(x)=\sin ωx+λ\cos ωx$, the distance from one of its symmetric centers to the nearest symmetric axis is $\frac{π}{4}$, and it reaches its maximum at $x=\frac{π}{12}$.
(1) Find the value of $λ$.
(2) If $g(x)=af(x)+\cos (4x-\frac{π}{3})$ is an increasing function on the interval $(\frac{π}{4},\frac{π}{3})$, find the range of values for $a$.

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