
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 a regular tetrahedron $ABCD$ with an edge length of $\sqrt {6}$, point $P$ is taken on the side edge $AB$ (not overlapping with $A$ or $B$). Determine the minimum value of $\frac {4}{a}+ \frac {1}{b}$, where $a$ is the distance from point $P$ to plane $BCD$ and $b$ is the distance from point $P$ to plane $ACD$.

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