
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
Tom has a scientific calculator. Unfortunately, all keys are broken except for one row: 1, 2, 3, + and -.
Tom presses a sequence of  $5$  random keystrokes; at each stroke, each key is equally likely to be pressed.  The calculator then evaluates the entire expression, yielding a result of  $E$ .  Find the expected value of  $E$ . 
(Note: Negative numbers are permitted, so 13-22 gives  $E = -9$ . Any excess operators are parsed as signs, so -2-+3 gives  $E=-5$  and -+-31 gives  $E = 31$ .  Trailing operators are discarded, so 2++-+ gives  $E=2$ .  A string consisting only of operators, such as -++-+, gives  $E=0$ .)

*Proposed by Lewis Chen*

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