
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 $ABCD$ be a regular square pyramid with vertex $P$ and a square base $ABCD$. Let $E$ be a point inside the square $ABCD$ but not at the centroid. Denote by $s$ the sum of the distances from $E$ to the faces $PAB$, $PBC$, $PCD$, $PDA$, and $ABCD$. Denote by $S$ the sum of the distances from $E$ to the edges $AB$, $BC$, $CD$, and $DA$. Find the ratio $\frac{s}{S}$.

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