
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
Let $P$ be a point inside $\triangle ABC$, where the altitudes from the vertices to the opposite sides are $h_A$, $h_B$, and $h_C$ respectively. The distances from point $P$ to the sides of the triangle are $l_a$, $l_b$, and $l_c$ respectively. Find the relationship between these distances. By analogy in three-dimensional space, let $P$ be a point inside a tetrahedron $ABCD$, with the distances from the vertices to the opposite faces being $h_A$, $h_B$, $h_C$, and $h_D$, and the distances from point $P$ to the four faces being $l_a$, $l_b$, $l_c$, and $l_d$ respectively. Find the relationship between these distances.

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