
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
From the set of integers $\{1, 2, 3, \dots, 150\}$, choose $k$ pairs $\{a_i, b_i\}$ with $a_i < b_i$ so that no two pairs have a common element. Suppose that all the sums $a_i + b_i$ are distinct and less than or equal to 150. Find the maximum possible value of $k$.

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