
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 $f(x) = A \sin(ωx + φ)$, where $(A > 0, ω > 0, |φ| < \frac{π}{2})$, the highest point $D$ has coordinates $(\frac{π}{8}, 2)$. When moving from point $D$ to the adjacent lowest point, the function intersects with the $x$-axis at point $(\frac{3π}{8}, 0)$.

1. Find the analytic expression of $f(x)$.
2. Find the interval where $f(x)$ is strictly increasing.

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