
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
Given a real number  $\alpha$ , a function  $f$  is defined on pairs of nonnegative integers by $f(0,0) = 1, f(m,0) = f(0,m) = 0$  for  $m > 0$ , $f(m,n) = \alpha f(m,n-1)+(1- \alpha)f(m -1,n-1)$  for  $m,n > 0$ .
Find the values of  $\alpha$  such that  $| f(m,n)| < 1989$  holds for any integers  $m,n \ge 0$ .

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