
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  $m$  be a positive integer, and let  $a_0, a_1,\ldots,a_m$  be a sequence of reals such that  $a_0=37$ ,  $a_1=72$ ,  $a_m=0$ , and \[a_{k+1}=a_{k-1}-\frac{3}{a_k}\] for  $k=1,2, \dots, m-1$ . Find  $m$ .

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