
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 smallest constant  $ C$  such that for all real  $ x,y$ 
\[ 1\plus{}(x\plus{}y)^2 \leq C \cdot (1\plus{}x^2) \cdot (1\plus{}y^2)\]
holds.

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