
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
Suppose the polynomial  $f(x) = x^{2014}$  is equal to  $f(x) =\sum^{2014}_{k=0} a_k {x \choose k}$  for some real numbers  $a_0,... , a_{2014}$ . Find the largest integer  $m$  such that  $2^m$  divides  $a_{2013}$ .

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