
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 tetrahedron $ABCD$, with $P$ as an interior point, and the distances $a'$, $b'$, $c'$, $d'$ from $P$ to the faces and $a$, $b$, $c$, $d$ from the vertices to the faces, find the value of $\frac{a'}{a} + \frac{b'}{b} + \frac{c'}{c} + \frac{d'}{d}$.

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