
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
Let $f(x)=a\sin 2x+b\cos 2x$, where $a$, $b\in\mathbb{R}$, $ab\neq 0$. If $f(x)\leqslant |f\left( \frac {\pi}{6}\right)|$ holds for all $x\in\mathbb{R}$, then  
(1) $f\left( \frac {11\pi}{12}\right)=0$;  
(2) $|f\left( \frac {7\pi}{12}\right)| < |f\left( \frac {\pi}{5}\right)|$;  
(3) $f(x)$ is neither an odd function nor an even function;  
(4) The interval of monotonic increase for $f(x)$ is $\left[k\pi+ \frac {\pi}{6},\;k\pi+ \frac {2\pi}{3}\right]\;(k\in\mathbb{Z})$;  
(5) There exists a line passing through the point $(a,b)$ that does not intersect the graph of the function $f(x)$.  
Among the above conclusions, the correct ones are \_\_\_\_\_\_ (Write down the numbers of all correct conclusions).

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