
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
In $\triangle ABC$, the sides opposite to angles A, B, C are $a$, $b$, $c$ respectively. Given $\overrightarrow {m}$=($c\cos C$, $\sqrt {3}$), $\overrightarrow {n}$=($2$, $a\cos B+b\cos A$), and $\overrightarrow {m} \perp \overrightarrow {n}$.
(1) If $c^2$=($5+2 \sqrt {3}$) $b^2$, $S_{\triangle ABC}$= $\frac {1}{2}$, find the values of $a$ and $b$.
(2) If $\lambda \sin 4A = \sin 2A + \cos 2A$, find the minimum value of the real number $\lambda$.

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