
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
 $a,b,c,d,e$  are equal to  $1,2,3,4,5$  in some order, such that no two of  $a,b,c,d,e$  are equal to the same integer. Given that  $b \leq d, c \geq a,a \leq e,b \geq e,$  and that  $d\neq5,$  determine the value of  $a^b+c^d+e.$ 

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