
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  $H$  be a rectangle with angle between two diagonal  $\leq 45^{0}$ . Rotation  $H$  around the its center with angle  $0^{0}\leq x\leq 360^{0}$  we have rectangle  $H_{x}$ . Find  $x$  such that  $[H\cap H_{x}]$  minimum, where  $[S]$  is area of  $S$ .

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