
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
The Fibonacci numbers  $F_1, F_2, F_3, \ldots$  are defined by  $F_1 = F_2 = 1$  and  $F_{n+2} = F_{n+1} + F_n$  for each integer  $n \ge 1$ . Let  $P$  be the unique polynomial of least degree for which  $P(n) = F_n$  for all integers  $1 \le n \le 10$ . Compute the integer  $m$  for which \[P(100) - \sum_{k=11}^{98} P(k) = \frac{m}{10} \dbinom{98}{9} + 144.\]

*Proposed by Michael Tang*

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