
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  $n$  be natural number and  $1=d_1<d_2<\ldots <d_k=n$  be the positive divisors of  $n$ . 

Find all  $n$  such that  $2n = d_5^2+ d_6^2 -1$ .

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