
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
Two math students play a game with  $k$  sticks. Alternating turns, each one chooses a number from the set  $\{1,3,4\}$  and removes exactly that number of sticks from the pile (so if the pile only has  $2$  sticks remaining the next player must take  $1$ ). The winner is the player who takes the last stick. For  $1\leq k\leq100$ , determine the number of cases in which the first player can guarantee that he will win.

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