
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
Jason and Jared take turns placing blocks within a game board with dimensions  $3 \times 300$ , with Jason going first, such that no two blocks can overlap. The player who cannot place a block within the boundaries loses. Jason can only place  $2 \times 100$  blocks, and Jared can only place  $2 \times n$  blocks where  $n$  is some positive integer greater than 3. Find the smallest integer value of  $n$  that still guarantees Jason a win (given both players are playing optimally).

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