
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 $A, R, M,$ and $L$ be positive real numbers such that
\begin{align*}
\log_2 (AL) + \log_2 (AM) &= 5, \\
\log_2 (ML) + \log_2 (MR) &= 6, \\
\log_2 (RA) + \log_2 (RL) &= 7.
\end{align*}
Compute the value of the product $ARML$.

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