
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
Given real numbers  $x,y,z,t\in (0,\pi /2]$  such that   $$ \cos^2 (x)+\cos^2 (y) +\cos^2 (z) +\cos^2 (t)=1. $$  What is the minimum possible value of   $$ \cot (x) +\cot (y) +\cot (z) +\cot (t)? $$  

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