
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
Determine the serial number(s) of the true proposition(s) below:

$①$ If $α+β= \dfrac {7π}{4}$, then $(1-\tan α)⋅(1-\tan β)=2$;

$②$ Given vectors $\overrightarrow{a}=(1,-2)$ and $\overrightarrow{b}=(2,λ)$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is acute, the range of the real number $λ$ is $λ < 1$;

$③$ Given point $O$ is a fixed point on a plane, and points $A$, $B$, and $C$ are not collinear on the plane. If moving point $P$ satisfies $\overrightarrow{OP}= \overrightarrow{OA}+λ( \overrightarrow{AB}+ \overrightarrow{AC})$, where $λ∈(0,+∞)$, then the trajectory of $P$ passes through the centroid of $\triangle ABC$;

$④$ In $\triangle ABC$, $\angle A=60^{\circ}$, and the lengths of sides $a$ and $c$ are $a=4$ and $c=3 \sqrt {3}$, respectively. Then, $\triangle ABC$ has only one solution;

$⑤$ If $\triangle ABC$ is inscribed in a circle with radius $R$, and $2R(\sin ^{2}A-\sin ^{2}C)=( \sqrt {2}a-b)\sin B$, the maximum area of $\triangle ABC$ is $\dfrac { \sqrt {2}+1}{2}R^{2}$;

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