
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 the largest constant $k$ such that for all real numbers $a, b, c, d$ in the interval $[0,1]$, the inequality $a^{2} b+b^{2} c+c^{2} d+d^{2} a+4 \geqslant k\left(a^{3}+b^{3}+c^{3}+d^{3}\right)$ holds.

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