
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 $B,$ $S,$ $N,$ and $T$ be positive real numbers such that
\begin{align*}
\log_{10} (BS) + \log_{10} (BT) &= 3, \\
\log_{10} (NT) + \log_{10} (NS) &= 4, \\
\log_{10} (SB) + \log_{10} (ST) &= 5.
\end{align*}
Compute the value of the product $BSNT.$

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