
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  $a$ ,  $b$ ,  $c$ ,  $d$ ,  $e$  be real strictly positive real numbers such that  $abcde = 1$ . Then is true the following inequality:  $$ \frac{de}{a(b+1)}+\frac{ea}{b(c+1)}+\frac{ab}{c(d+1)}+\frac{bc}{d(e+1)}+\frac{cd}{e(a+1)}\geq \frac{5}{2} $$  

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