
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 $$f(x)=-2\sin(3x+ \frac {π}{4})+5$$.

1. Find the intervals where $f(x)$ is strictly increasing.
2. Find the center of symmetry.
3. Find the minimum value of $f(x)$ and the set of corresponding $x$ values where this minimum is achieved.

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