
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 vectors **_a_**, **_b_**, and **_c_** satisfy **_a_** + **_b_** + **_c_** = 0, (**_a_** - **_b_**)⊥**_c_**, and **_a_**⊥**_b_**. If |**_a_**| = 1, then the value of |**_a_**|^2 + |**_b_**|^2 + |**_c_**|^2 is ______.

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