
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  $a_1$ ,  $a_2$ ,  $a_3$ ,  $a_4$ ,  $a_5$  be real numbers satisfying
\begin{align*}
  2a_1+a_2+a_3+a_4+a_5 &= 1 + \tfrac{1}{8}a_4 
      2a_2+a_3+a_4+a_5 &= 2 + \tfrac{1}{4}a_3 
          2a_3+a_4+a_5 &= 4 + \tfrac{1}{2}a_2 
              2a_4+a_5 &= 6 + a_1
\end{align*}
Compute  $a_1+a_2+a_3+a_4+a_5$ .

*Proposed by Evan Chen*

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