
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
How many tuples of integers  $(a_0,a_1,a_2,a_3,a_4)$  are there, with  $1\leq a_i\leq 5$  for each  $i$ , so that  $a_0<a_1>a_2<a_3>a_4$ ?

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