
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
Define: $min\{x, y\}$ as the smaller number among the real numbers $x$ and $y$. Given $$h=min\left\{a, \frac {b}{a^{2}+4b^{2}}\right\}$$, where $a, b$ are positive real numbers, then the maximum value of $h$ is \_\_\_\_\_\_.

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