
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
Let \( f(x, y) = a(x^3 + 3x) + b(y^2 + 2y + 1) \) and suppose that \( 1 \leq f(1,2) \leq 2 \) and \( 2 \leq f(3,4) \leq 5 \). Determine the range of \( f(1,3) \).

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