
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 $f(x)= \sqrt {3}\sin (\omega x+\varphi)+2\sin ^{2} \frac {\omega x+\varphi}{2}-1$ $(\omega > 0,0 < \varphi < \pi)$ is an odd function, and the distance between two adjacent axes of symmetry is $\frac {\pi}{2}$.  
(1) When $x\in(- \frac {\pi}{2}, \frac {\pi}{4})$, find the decreasing interval of $f(x)$;  
(2) Translate the graph of the function $y=f(x)$ to the right along the $x$-axis by $\frac {\pi}{6}$ units, and then shorten the abscissa to half of its original length (the ordinate remains unchanged), to obtain the graph of the function $y=g(x)$. When $x\in[- \frac {\pi}{12}, \frac {\pi}{6}]$, find the range of the function $g(x)$.  
(3) Given that $x= \frac {\pi}{6}$ is an axis of symmetry for the function $h(x)=f(x)+\lambda\cos 2x$, find the value of $\lambda$.

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