
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 $f(x)=\sin (ωx+φ)(ω > 0,0 < φ < \dfrac {π}{2})$ whose graph passes through the point $(0, \dfrac {1}{2})$, and the distance between two adjacent symmetry axes is $\dfrac {π}{2}$.
(1) Find the analytical expression of the function $f(x)$ and its monotonically increasing interval in $[0,π]$;
(2) In $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to $A$, $B$, $C$ respectively. If $f( \dfrac {A}{2})-\cos A= \dfrac {1}{2}$, $bc=1$, $b+c=3$, find the value of $a$.

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