
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 following propositions:
$(1)$ The graph of $y=\cos (x- \frac {π}{4})\cos (x+ \frac {π}{4})$ is symmetrical about the line $x= \frac {π}{2}$;
$(2)$ The graph of $y= \frac {x+3}{x-1}$ is symmetrical about the point $(-1,1)$;
$(3)$ The quadratic equation $ax^{2}-2ax-1=0$ has exactly one real root, then $a=-1$;
$(4)$ There are two triangles $\triangle ABC$ that satisfy the conditions $AC= \sqrt {3}$, $\angle B=60^{\circ}$, $AB=1$.
Determine the sequence number(s) of the true proposition(s).

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