
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
Suppose  $a$ ,  $b$ ,  $c$ , and  $d$  are positive real numbers which satisfy the system of equations \[\begin{aligned} a^2+b^2+c^2+d^2 &= 762,  ab+cd &= 260,  ac+bd &= 365,  ad+bc &= 244. \end{aligned}\] Compute  $abcd.$ *Proposed by Michael Tang*

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