
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 $f(x) = A\sin(ωx + φ) + B$ $(A > 0, ω > 0, |φ| < \frac{π}{2})$ with a maximum value of $2\sqrt{2}$, a minimum value of $-\sqrt{2}$, a period of $π$, and passing through the point $(0, -\frac{\sqrt{2}}{4})$.

1. Find the analytical expression of the function $f(x)$.
2. Find the interval where the function $f(x)$ is monotonically increasing.

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