
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 $VABCD$ be a right square pyramid with $V$ as the apex and $ABCD$ as a square base. Let $P$ be a point inside square $ABCD$. Denote by $t$ the sum of the distances from $P$ to the triangular faces $VAB, VBC, VCD, VDA$, and by $U$ the sum of the distances from $P$ to the sides $AB, BC, CD, DA$ of the square. Calculate the ratio $\frac{t}{U}$.

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