
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
Find all reals  $ k$  such that
\[ a^3 \plus{} b^3 \plus{} c^3 \plus{} d^3 \plus{} 1\geq k(a \plus{} b \plus{} c \plus{} d)
\]
holds for all  $ a,b,c,d\geq \minus{} 1$ .

*Edited by orl.*

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