
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 $f(x)=2\cos (ωx+φ)(ω > 0,0 < φ < \dfrac {π}{2})$ with a minimum positive period of $π$, and the point $(\dfrac {5π}{24},0)$ being a symmetry center of its graph.
1. Find the interval where the function $f(x)$ is monotonically increasing;
2. In $△ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively. If $f(-\dfrac {A}{2})= \sqrt {2}$, $a=3$, find the maximum value of $b+c$.

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