
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 \( f(x) = ax^3 + bx^2 + cx + d \) ( \( a \neq 0 \), \( a \), \( b \), \( c \), \( d \in \mathbb{R} \) ). Given \( 0 < 2f(2) = 3f(3) = 4f(4) < 1 \), find the range of values for \( f(1) + f(5) \).

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