
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 positive real numbers $P,$ $Q,$ $S,$ $T$ such that:
\[
\log_{10} (PS) + \log_{10} (PT) = 3, \\
\log_{10} (ST) + \log_{10} (SQ) = 4, \\
\log_{10} (QP) + \log_{10} (QT) = 5.
\] 
Compute the value of the product $PQST.$

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